Jacobs, Jr., M., and Karagozoglu, A, 2011 ... - Michael Jacobs Jr

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May 21, 2011 - Moody's All-Corporate default rate and reported similar behavior. However ...... Moody's Investor Service, December 2003. Fama, E.F., and K.R. ...
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Modeling Ultimate Loss Given Default on Corporate Debt

A hmet K. K aragozoglu

Au Summer 2011

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coherent ­t heoretical underpinning, a continuing challenge to researchers. This study contributes to the research on LGD on several fronts. The review of literature considers recent contributions and combines many elements into a unified empirical framework. The methodology builds an internally consistent model of LGD that corresponds to a priori expectations and empirical findings, which is amenable to rigorous validation and represents an advance in econometric methodology. In particular, estimation of a two-equation system models LGD simultaneously at the obligor and instrument levels, using an extensive sample of corporate bond and loan defaults. In addition to answering the many academic questions regarding LGD, we provide a practical tool for risk managers, traders, and regulators in the field of credit. For example, these players in the credit markets can use our model to forecast ultimate LGD, which can serve as input into credit models for value at risk (VaR), distressed debt pricing, or regulatory capital. LGD can be defined variously depending upon the institutional setting, the type of instrument (e.g., traded bonds or bank loans), or the credit risk model (e.g., pricing debt instruments subject to the risk of default, expected loss calculation or credit risk capital). The ultimate LGD represents eventual discounted loss per dollar of ­outstanding balance at default. When considering loans that

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is an associate professor at the Zarb School of Business at Hofstra University in Hempstead, NY. [email protected]

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oss given default (LGD), the loss severity on defaulted debt obligations, is a critical component of risk management, pricing, and portfolio models of credit.1 LGD is among the three primary determinants of credit risk, the other two being probability of default (PD) and exposure at default (EAD). However, LGD has not been as extensively studied and is considered a much greater modeling challenge than PD. Traditional credit models such as PD have focused on systematic components of credit risk that attract risk premiums. Unlike PD, determinants of LGD have typically been ascribed to idiosyncratic, borrower-specific factors. However, there is now an ongoing debate about whether the risk premium on defaulted debt should ref lect systematic risk and, in particular, whether the intuition that LGDs would rise in worse states of the world is correct; and how this could be refuted empirically given limited and noisy data. This heightened focus on LGD has been motivated by the large number of defaults and nearly simultaneous decline in recovery values observed through the last credit cycle as well as the current credit crisis, regulatory developments such as Basel II (Basel Committee of Banking Supervision [2005]), and the continued growth in credit markets. However, obstacles to better understanding and predicting LGD include a dearth of relevant data and the lack of a

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is senior financial economist in the Credit Risk Modeling Division of the Office of the Comptroller of the Currency, U.S. Department of the Treasury in Washington, DC. [email protected]

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M ichael Jacobs, Jr.,

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Michael Jacobs and Ahmet K. Karagozoglu

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the application of credit models and estimation of LGD from available data. This literature ranges from simple quantification of LGD, to calibration of credit models embedding LGD assumptions, to empirical or vendor models of LGD. The Zeta model of Altman, Haldeman, and Narayanan [1977] was a second generation of the Altman Z-score PD estimation model. In this model, loan LGD estimates were based on a workout department survey (1971–1975), which yielded conclusions regarding the magnitude of discounted post-restructuring recoveries on unsecured bank loans. Bank studies focusing on internal loan data included research by JP Morgan Chase (Araten, Jacobs, Jr., and Varshney [2004]), where the authors studied ultimate workout LGD for wholesale loans during 1982 through 2000. Among early studies relying almost exclusively on secondary market prices of bonds or loans soon after the time of default, Altman and Kishore [1996] estimated LGDs for defaulted senior secured and senior unsecured bonds from 1978 to 1995, yielding estimates that could be statistically distinguished among various industry groups. Altman and Eberhart [1994] and Fridson, Garman, and Okashima [2000] provided evidence that the more senior bonds significantly outperformed the more junior bonds in the post-default period, results confirmed by Hamilton, Gupton, and Berthault [2001] for secondary market loan prices a month after default. Emery [2003] and Altman and Fanjul [2004] compared LGDs on bank loans and bonds, respectively, as inferred from the prices of the traded instruments at default in a Moody’s database, revealing that loans experience lower loss severities when controlling for seniority. Cantor, Hamilton, and Varma [2003] showed similar findings for corporate bonds as Altman and Fanjul and additionally found differential LGD by rating at origination, such that “fallen angels” of the same seniority had significantly lower LGDs.3 Among studies that looked at ultimate LGD, Standard and Poor’s (Keisman and van de Castle [2000]) presented empirical results from the LossStatsTM in the 1987–1996 period for marketable bonds and loans. This study also showed that the inf luence of position in the capital structure (i.e., the proportion of debt above or below a claimant in bankruptcy) was independent of collateral and seniority in determining loss severities. A more recent rating agency study by Moody’s (Cantor and Varma [2004]) examined the determinants of ultimate LGD for North American corporate issuers over a

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may not be traded, and taking into consideration when cash was received as well as other losses incurred in the collection process, ultimate LGD is the relevant measure for an input into a regulatory or economic credit capital model. In the case of bonds or marketable loans, one can measure the prices of traded debt at the initial credit event, or the discounted market values of instruments received at the resolution of default. The latter is potentially a proxy for the ultimate LGD, the focus of our study for two purposes. Our primary objective is to provide results of use to agents invested in defaulted securities having time horizons that span the resolution period, who wish to assess expected value upon emergence relative to some benchmark available at default, such as trading or model-based prices. Agents who would benefit include bank workout specialists, risk managers, or vulture hedge fund investors. Second, our results would be relevant for financial institutions attempting to quantify economic LGD for purposes of the Basel II Advanced IRB approach to regulatory capital, which requires estimation of the ultimate LGD. Aspects of this modeling exercise deserving of special attention include the distributional properties of LGD. While the available theory and empirical evidence suggests it to be stochastic and predictable with respect to other variables, in most extant credit models LGD has been treated as either deterministic or as an exogenous stochastic process. The quest for tractability gives rise to such assumptions, but in practical applications this results in understated capital, mispricing, and unrealistic dynamics of model outputs. Our research helps to resolve such deficiencies by modeling ex ante the distribution of LGD as a function of empirical determinants such as contractual features, firm capital structure, ­borrower characteristics, debt and equity market variables, and systematic factors. In order to empirically investigate the determinants of, and build predictive econometric models for, ultimate LGD, we use an extensive sample of 871 defaulted firms (covering 1985 to 2008), a dataset containing the complete capital structures of each obligor. Our sample is highly representative of the U.S. large corporate loss experience over the last two decades. LGD has been a relatively neglected aspect of credit risk research.2 Starting with the seminal work by Altman [1968], modeling of PD is currently in a relatively mature stage as compared to LGD. The ­heightened focus on LGD is evidenced by the recent f lurry of research into 2    Modeling Ultimate Loss Given Default on Corporate Debt

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and Srinivasan [2007] examined the same data and time period as Keisman and van de Castle [2000], and while they verified that seniority and security are key determinants of LGD, in addition they found industry-specific factors inf luencing LGD independently of the macroeconomic state and bond market conditions analyzed in Altman et al. [2005]. In particular, after controlling for firm-specific, contractual, and systematic factors they found elevated LGDs in distressed industries, defined as those sectors having significantly lower profitability than the overall market. They argued that in these cases fewer re-deployable assets, greater leverage, and lower liquidity are driving lower average recoveries and that their results support a test of the Schleifer and Vishny [1992] “firesale” hypothesis, an industry equilibrium phenomenon in which macro and bond market variables are spuriously significant due to omitting an industry factor. Among studies similar to ours, Carey and Gordy [2007] argued for a two-stage approach to measuring LGD, first estimating an “estate LGD” at the obligor level and then treating instrument-level LGDs according to a contingent claims approach, as under APR such recoveries can be viewed as collar options on residual value of the firm. However, they argued that the endogeneity of the bankruptcy decision would result in a measurement problem in the first-stage borrower level. Furthermore, an extensive literature on violations of APR suggested a similar problem in the second-stage instrument level (Eberhart, Moore, and Rosenfeldt [1989]; Hotchkiss [1993]; Weiss [1990]). The authors also addressed the issue of whether systematic variation in LGD could be refuted given data limitations, in particular the large proportion of unexplained variation in the cross-section of recovery cash-f lows. Finally, we make note of this evidence regarding the PD–LGD correlation inf luencing the Basel II guidelines: paragraph 468 on downturn LGD in the Bank for International Settlements (BIS) Accord (Basel Committee of Banking Supervision [2003, 2004]) and the additional guidance offered by the BIS (Basel Committee of Banking Supervision [2005]). Basel II requires advanced internal ratings based (IRB) banks to capture all relevant risks regarding possible cyclical variability in LGD, and at the same time it states that bank estimates of long-term ultimate LGDs having no such ­systematic variations may be acceptable. Miu and Ozdemir [2006] argued that banks can incorporate conservatism into cyclical LGDs estimated in a point-in-time framework

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period of 21 years (1983–2003), looking at many of the variables considered herein (e.g., seniority and security; firm/industry-specific and macroeconomic factors). Several recent empirical studies of LGD attempting to measure LGD–PD correlation have put more ­structure around this exercise, either by building predictive econometric models or by attempting to directly test models. Frye [2000a, 2000b, 2000c] examined the LGD–PD correlation in extensions of the Merton [1974] framework allowing for systematic recovery risk and found a significant negative relationship at various levels of aggregation. Other studies examined this by looking at LGD as implied from the prices of traded debt at or prior to default, as opposed to ultimate LGD, or the “reducedform” approach. Among these, Jarrow [2001] developed a hybrid structural–reduced model, in which PDs and LGDs were functions of the underlying state of the macro-economy. Hu and Perraudin [2002] also examined this relationship and found LGD–PD correlations on the order of 20%. Jokivuolle and Peura [2003] presented an option theoretic model for bank loans and were able to produce a positive correlation between PD and LGD. Bakshi et al. [2001] extended the reduced-form approach by allowing a f lexible correlation between PD, LGD, and the risk-free rate. Imposing a negative correlation between PD and LGD, they found that a 4% increase in the (risk-neutral) hazard rate was associated with a 1% increase in the expected LGD. In related work on the resolution of default focusing on high-yield debt portfolios, Parnes [2009] developed a theoretical model that explicitly incorporated LGD assumptions. Several studies showed that LGDs tend to rise more in periods of recession than they fall during expansions, suggesting that more is at play than a macroeconomic factor inf luencing the value of collateral. Keisman and van de Castle [2000] found that during the earlier stress period at the beginning of the previous decade, LGDs of all seniorities rose in the S&P LossStatsTM database for the 1982–1999 period. Altman, Resti, and Sironi [2001, 2003] also found that LGDs increase as the credit cycle worsens and as default rates increase above the cycle’s long-run average.4 Araten et al. [2004] related unsecured U.S. large corporate borrower-level LGDs to the average Moody’s All-Corporate default rate and reported similar behavior. However, Altman, Brooks, Resti, and Sironi [2005] found that a systematic variable had no effect on LGD when controlling for bond market conditions (e.g., supply–demand imbalances). Acharya, Bharath, Summer 2011

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expectation of yi depends upon a linear function h of the xi only through a smooth, invertible function m: 1

EP  yi |xi  = µ = ∫ p ( yi |xi )yi d υ ( yi ) = m ( η)



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η = βT xi = m −1 ( µ )



(2)



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p ( yi |xi ,β, Ai ,ζ )

A  ζ  = exp  i yi θ ( xi |β ) − γ ( xi |β ) + τ  yi ,    Ai    ζ

}

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{

(3)

where g(⋅) and t(⋅)are smooth functions (satisfying certain regularity conditions), Ai is a known prior weight, V ∈ R + is a scale parameter (possibly known), and the location function J(⋅) is related to the linear predictor according to:

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Econometric Modeling

(1)

where m -1(⋅) is defined as the link function that maps from the conditional mean of the response variable m to the linear function h(⋅). Then the distribution of yi resides in the exponential family, which implies a probability distribution function of the following form:

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without an LGD–PD correlation; however, they estimated commensurate increases in credit capital to compensate for this. Our approach extends the existing research along several dimensions. First, we contribute to prior work by modeling LGD jointly at the firm and instrument levels. In particular, a simultaneous equation estimation of LGD at the instrument and obligor levels is advantageous in that we can model enterprise value coherently, which is understood by market participants in the large-corporate sector of the distressed and defaulted debt market to be a key determinant of recoveries. That is, under the assumption of a strict absolute priority rule (APR), recovery on an instrument residing somewhere in the capital structure of a firm can be likened to a collar option—there is positive recovery only if it is “in the money” or when enterprise value is sufficient to satisfy all superior claims. Second, as compared to extant work, we integrate new variables with those previously considered into a unified framework; including the cumulative-abnormal returns (CARs) on borrower’s equity prior to default, which decreases the ultimate LGD, size of the defaulted firm, and market price of distressed debt at default. Finally, in addition to these we confirm many of the findings of the literature in regard to determinants of LGD such as contractual, capital structure, firm-specific features, industry characteristics, and macroeconomic considerations.



( (

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(

θ ( xi |β ) = ( γ ′ )−1 µ ( xi ) = ( γ ′ )−1 m βT xi

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(4)

This framework subsumes many of the models in the literature on the classical linear regression and limited/qualitative dependent variables framework. Here we consider the case most relevant for LGD estimation and least pursued in the GLM literature. In this context, we are dealing with a random variable in a bounded region, the unit interval. This is most conveniently modeled through employing a beta distribution, in which case we denote the response percent loss rate as li ∈ [0,1]. As in Mallick and Gelfand [1994], we take the link function to be a mixture of cumulative beta distributions:

where B [ x, y ] = ΓΓ( x( x)Γ+y( y) ) = ∫ 10 u x −i (1 − u )y −1 du in Equation (5) is the standard beta function, G(x) =x! is the gamma function, and the parameters j,a,b are chosen to match features of the data.6 While in most cases we do not have a closed-form solution, we can always estimate

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To predict and estimate distributional characteristics of LGD, in our empirical analysis we utilize the beta-link generalized linear model (BLGLM), which is in the class of generalized linear models (GLMs) that encompass the logistic, truncated normal, and Tobit models. These models have been used mainly in understanding and quantifying economic relationships, as well as having been employed in prediction, both of which are of importance in the modeling of LGD. However, much of the literature has focused upon qualitative dependent variables, into which the case of PD estimation naturally falls. Maddala [1983, 1991] introduced, discussed, and formally compared the different models.5 The ith observation of the dependent (or response) variable, the ultimate LGD, is denoted by yi. The vector of independent variables corresponding to yi is denoted by xi = (x1i , … xpi )T. We assume that the conditional

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η( xi |β, ϕ, a,b ) = β xi = ∑ φ j T

j =1

li



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a j −1

(1 − u )

b j −1

B a j ,b j 

du

(5)

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the underlying parameters b consistently and efficiently by maximizing the log-likelihood function: l ( θ(β|xi ),ζ(β|xi ),β|xi , yi , Ai ) n  Ai = ∑ y i θi ( β | x i ) − γ ( β | x i ) i =1  ζ (β|x i )  ζ[β|xi ]   + τ  yi ,  Ai   

Data and Summary Statistics

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We are able to obtain global convergence through optimizing Equation 6 across observations in our dataset, as discussed in subsequent sections.7 This approach has the benefit of the capability to model the highly bimodal nature of the distribution rather accurately, without recourse to more complex, less transparent (or replicable), more computationally demanding, and less stable alternatives such as non-parametric approaches (Renault  and Scailett [2003]) or maximum-entropy (Friedman and Sandow [2003]).

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(6)

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We have built a database of defaulted firms representative of the U.S. large corporate loss experience (bankruptcies and out-of-court settlements), all having Moody’s rated instruments at some point prior to default. Our database is constructed through merging the December 2008 release of the Moody’s Ultimate Recovery Database™ (MURD) with information from various sources such as www.Bankruptcy.com, Edgar SEC filings, LexisNexis, Bloomberg, Compustat, and the Center for Research in Security Prices (CRSP). It contains data on 3,902 defaulted instruments from 1986 to 2006 for 871 borrowers, for which there is information on all classes of debt in the capital structure at the time of default. Despite our sample selection being driven mainly by data availability in the matching of the MURD database to other databases, the final dataset is largely representative of the U.S. large-corporate default experience over the last 20 years.8 All instruments are detailed by debt type, seniority, collateral type, position in the capital structure, original and defaulted amount, resolution outcome, and instrument price or value of securities at the resolution of default (emergence from Chapter 11 bankruptcy as an independent entity or acquisition by a third party, Chapter 7 liquidation or

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out-of-court settlement of a distressed exchange). It includes either the prices of pre-petition instruments at the time of emergence from, or prices of new instruments received in settlement of, bankruptcy or other distressed restructuring, respectively. For a subset of observations, we can obtain the prices of traded debt, the equity prices, or financial statement data at around the time of default.9 We calculate economic LGD by discounting nominal LGD by the coupon rate on the instrument prevailing just prior to default.10 Exhibit 1 presents the counts and sample averages of various key variables: trading instrument inferred LGD at default, discounted LGD, number of major creditor classes, principal at default, and time to final resolution. These are presented at the instrument level and the obligor level, and then further broken down among bankruptcies and out-of-court settlements. Most defaults are bankruptcies as opposed to out-of-court settlements, with 3,273 bankruptcies versus 629 settlements at the instrument level and 728 bankruptcies versus 143 ­out-of-court settlements at the obligor level. Our dataset contains the prices of traded debt available at the time of default for only 1,118 out of 3,902 (or 28.6%) of the instruments and for 460 out of 871 (or 52.8%) of the obligors. Average LGDs across the entire sample as inferred from the prices of traded instruments at default are significantly higher than ultimate LGDs, 61.04% versus 43.21% at the instrument level, and 63.46% versus 46.88% at the obligor level, consistent with previous research (Cantor, Emery, Keisman, and Ou [2007]).11 Discounted LGD is much higher for bankruptcies as compared with out-of-court settlements, 48.38% versus 16.31% at the instrument level, and 51.41% versus 23.80% at the obligor levels.12 We also see the marked non-normality of the LGD estimates, which is accentuated for the ultimate LGDs as compared to the trading prices, with standard deviations at the instrument level of 40.4% versus 28.7% and at the obligor level of 31.8% versus 23.9%. Firms in the database tend to have about two major creditor classes in a range from 1 to 6, with an average of 2.44 at the instrument level and 2.20 at the obligor level. Furthermore, and perhaps surprisingly, if we take this as a measure of the complexity of the capital structure, outof-court settlements do not tend to have fewer creditor classes than bankruptcies, an average of 2.55 versus 2.42 at the instrument level, and 2.31 versus 2.18 at the obligor level. Average time to resolution from first instrument The Journal of Fixed Income    5

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Exhibit 1

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Characteristics of LGD Observations by Default Type: Instrument vs. Obligor Level Analysis (Moody’s rated defaults, 1985–2008)

default to final instrument resolution is 1.38 years at the instrument level and 1.36 years at the obligor level. This is a long-tailed distribution, ranging from a day in some of these prepackaged bankruptcies or out-of-court settlements, to a 9.18-year bankruptcy resolution process. Out-of-court settlements resolve much more quickly, on average 0.21 years for the instrument level and 0.42 years for the obligor, and the range of the distribution is compressed, ranging from 0.002 to 5.64 years. Exhibit 2 presents distributional statistics and Spearman rank order correlations with LGD (both at the obligor and instrument levels) for selected variables in our database. We highlight qualitatively a few key statistics here that have economic meaning or relate to our final results, first considering borrower financial ratios. LGD is negatively correlated with leverage measures, a strongest effect for the ratio of total debt to market value of equity as compared to the ratio of total debt to book value. Variables measuring size, like book value of assets or market value of equity, correlate with LGD positively at the firm level and negatively at the instrument level. Tobin’s Q, a measure of the degree to which there may be unrecorded firm value, has relatively strong positive correlation with LGD at both obligor and instrument levels. The intangibles ratio (IR), which conveys similar information, also has positive correlations with LGD that are of greater magnitude at the obligor level. Variables measuring cash f low (working capital to total assets or operating cash f low ratios) are both negatively correlated with LGD at mild to reasonably strong levels. Measures of industry profitability (e.g., return on assets or profit margin) are moderately and negatively correlated with LGD. Among variables representing capital structure characteristics, number of

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Notes: LGD at Default = 1 minus the price of defaulted debt at the time of default; for obligors, weighted by the amounts outstanding at default. Discounted LGD = the ultimate dollar loss given default on the defaulted debt instrument: 1 minus recovery at emergence from bankruptcy or time of final settlement as a percent of par; alternatively, this can be expressed as (amount outstanding at default total ultimate dollar recovery)/(amount outstanding at default); for obligors, weighted by the amounts outstanding at default. Number of Creditor Classes = major creditor classes as defined by the bankruptcy court or by mutual agreement in the out-of-court settlement. Principal at Default = the total instrument or obligor outstanding at default. Time to Resolution = the time in years from the ( first) instrument default date to the time of ultimate recovery for instruments (obligors).

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Exhibit 2

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Summary Statistics on Selected Variables and Correlations with LGD (Moody’s rated defaults, 1985–2008)

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instruments, and number of creditor classes, the degree to which the firm’s debt is secured or the degree to which banks are represented in the creditor group is positively correlated with LGD. Considering variables measuring the amount of credit risk, the best predictor of ultimate LGD is the loss given default from the price of traded debt at default, having a very strong positive correlation. Cumulative abnormal returns (CAR)13 on equity prices in the 90 days until default (median of -12%) have the second strongest positive correlation to LGD. The number of downgrades prior to default is negatively correlated with the LGD, which could imply either that LGD is lower if obligors were originally more highly rated, or if the migration to default is more gradual. Correlations of variables capturing contractual

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features show that instruments having subordinated seniority ranks, inferior collateral quality segments, or thinner debt cushions have significantly higher LGDs, while the debt cushion measures have similarly strong relationships. In the set of variables measuring time spans of interest, we see rather strong relationships: time to maturity of defaulted instruments is positively related to discounted LGD, and time between defaults is negatively related to discounted LGD. Finally, we observe evidence that LGDs are elevated during downturns, as LGD is increasing (decreasing) in the Moody’s speculative-grade default rate (S&P 500 equity index return), consistent with the large body of empirical evidence as discussed previously in the literature review.

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In this section we discuss our empirical findings for the full information maximum likelihood estimation (FIMLE) of the beta link generalized linear model (BLGLM), a simultaneous equation analysis of instrument and obligor LGD. Exhibit 3 presents results from the FIMLE of the multivariate BLGLM model. FIMLE is used to model the endogeneity of the relationship between LGD at the obligor (firm) and instrument levels in an internally consistent manner. This technique enables us to build a model that can help us understand some of the structural determinants of LGD, and potentially improve our forecasts of LGD. All variables are economically significant, as well as statistically significant, in all cases at conventional confidence levels. We find that the financial statement and capital structure variables should only appear in the equation for obligor LGD, while the contractual feature variables should only appear in the instrument equation. There is a clear economic argument for this in that fundamental factors should inf luence the f irm-level recoveries, while structure of the loan determines to what extent the instrument is “in the money.” We also find that CARs and obligor level LGD at default best belong in the obligor equation and that instrument LGD at default and ultimate obligor LGD best belong in the instrument equation. The latter variable, ultimate obligor LGD in the ultimate instrument LGD equation, captures the feedback loop between the two dependent variables. In the macroeconomic category, all the variables are found to belong in the obligor equation. However, in some other categories we find no clear division, in that some variables were best excluded from one equation whereas others were best included in both within the same category. One case is the credit quality/market category, where investment grade at origination appears in the obligor equation, while principal at default appears only in the instrument equation. Another case is the vintage category, where time between defaults and time to maturity appear only in the obligor and instrument equations, respectively. Of the credit quality/market variables, the two most important determinants of the ultimate instrument LGD are the instrument LGD at default and the ultimate obligor LGD. To capture the feedback between the two levels of loss severity, we estimate partial effects of 0.21 and 0.19, respectively, which implies that for a

10% increase in either of these we can expect ultimate instrument LGD to increase by about 2%. This says that modeling instrument level recovery akin to a collar option on firm enterprise value does not give the whole story, as there is information about this also embedded in the distressed debt markets. In the obligor equation, for CAR we estimate a partial effect of -0.28 (i.e., if CARs are 30% higher, then ultimate obligor LGD is expected to be about 10% lower), so that there is additional information on the ultimate recovery encoded in the equity market. Our interpretation is that as the market makes a directionally correct assessment of future expected recoveries, trading patterns result that give rise to this price pattern: Arbitrageurs could be going long or short credit on the perceived better or worse equity of recovering issues from otherwise matched issuers nearing default.14 Principal at default is slightly less economically significant but no less meaningful, having a partial effect of about 0.001 in the instrument equation (i.e., as the loan amount increases by a factor of 10, LGD decreases by about 10%). This is interesting in that it confirms the hypothesis that loan size may be proxy for unobserved LGD determinants such as complexity of the workout process or coordination issues among creditors. In the context of Basel II, this speaks to the correlation between LGD and EAD, as evidence that post-default recovery risk may be positively correlated with exposure risk prior to default. Finally, the dummy for investment grade (at earliest rating date or origination), which only appears in the obligor equation, has a partial effect of -0.07. All else being equal, credits originally rated as investment grade have 7% lower estate level LGD, which is consistent with the well-known empirical finding that “fallen angels” have lower loss severities (Altman and Ramayanam [2006]). Among the set of variables measuring the effect of the business cycle, we observe that the dummy variables for the 2000–2002 and 1989–1991 recessionary episodes enter the obligor equation with partial effects of 0.17 and 0.11, respectively, so that LGD was on this order (17% and 11%) during these periods even after controlling for other systematic factors. This is evidence of contagion effects at play, or the phenomenon that there is more LGD risk than can be explained by observable factors due to either unobserved heterogeneity or clustering of defaults during stress periods (Lando and Nielson [2010]). The two other macro variables, Moody’s speculative default rate and the S&P 500 return, have partial effects of 0.07

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Empirical Results

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Exhibit 3

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Analysis of Simultaneous Equation Modeling of Discounted Instrument and Obligor LGD: Full Information Maximum Likelihood Estimation using Beta Link Generalized Linear Model (Moody’s rated defaults, 1985–2008)

Notes: This exhibit presents results from the full information maximum likelihood estimation (FIMLE) of the beta link generalized linear model (BLGLM) model for firm- and instrument-level LGD. FIMLE is used to model the endogeneity of the relationship between LGD at the firm and ­instrument levels in an internally consistent manner.

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results in about a 20% higher LGD. This sign is expected based upon prior research suggesting that defaulted firms whose defaulted assets are of a more tangible quality (e.g., utilities or heavy manufacturing) are more likely to generate better recoveries (Altman and Kishore [1996]). Operating cash f low exhibits considerable economic significance as well, having a partial effect of -8.31 × 10 -3, in line with our expectation that firms with a business that is fundamentally more viable are better able to rehabilitate through the resolution process, resulting in greater recovery cash f lows and lower ultimate LGDs. Finally for this group, the liquidity measure of working capital to total assets has a partial effect of -0.13. This may be similarly rationalized in that relatively robust cash f low or profitability—a measure of underlying viability of the defaulted obligor’s business prospects—could imply a more successful resolution process and superior recoveries (Jacobs et al. [2010]). Considering industry-specific factors, we first see that industry profit margin has a partial effect of -0.092, consistent with the Acharya et al. [2007] firesale effect. The dummy variable for the technology has partial effects of 0.06 at the instrument level and 0.03 at the obligor level. The dummy for the utility industry, appearing only in the obligor equation, has a partial effect of -0.15. The latter results, which hold above and beyond the macroeconomic covariates appearing in the regression, are further evidence of the independent importance of industry-specific factors in explaining LGD and the plausibility of a separate systematic factor governing LGD apart from that driving default (Frye [2000a, 2000b, 2000c]). The results for the contractual loan structure variables appearing only in the instrument equation tell a similar story as the financial variables just discussed, both in terms of quality of estimates and congruence of signs on coefficients with our prior expectations. The dummy variables for creditor class, with the base class being bank debt, are all of expected sign and all statistically significant, with partial effects of 0.04, 0.07, 0.23, and 0.11 for senior secured, senior unsecured, senior subordinated, and junior subordinated, respectively. The results for collateral rank are also robust in terms of economic and statistical significance, with a partial effect of 0.15. This ref lects the previous findings and intuition that more senior and better-secured instruments have better recoveries (Altman [2006]). Finally for this group, the ­coefficient estimates on proportion of

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and 0.14, respectively. Therefore, a doubling of default rates increases LGD by about 14%, while a 10% increase in the stock market reduces LGD by about 1%. In the case of the variables measuring the legal setting, the economic impact of bankruptcy filing is measured by a partial effect of 0.14, so that firms entering Chapter 11 have 14% higher LGDs than those who default and renegotiate their debt. On the other hand, the indicator for a pre-packaged bankruptcy has a partial effect of -0.04, which means that these firms have 4% lower LGD on average. These results are in line with much of the literature on the resolution mechanisms and outcomes with respect to default or financial distress ( Jacobs et al. [2010]). Now let us consider the financial variables appearing only in the obligor equation. The scale variable book value is statistically significant with a negative sign on the coefficient estimate, a partial effect of -0.08, so that firms an order of magnitude larger by this measure have 8% lower ultimate LGD. It may be argued that a larger firm may have the wherewithal to more successfully navigate a default and be rehabilitated due to various factors associated with size (e.g., market power, government support), which is associated with superior recoveries (Jacobs et al. [2010]). The leverage variable debt-to-equity ratio has considerable economic impact, having a partial effect of -0.09, so that a doubling of leverage decreases loss severity by about 20%. At first, this result might seem counterintuitive, since leverage measures are closely related to probability of default (PD) in the Merton [1974] structural modeling framework. However, in the case of LGD this logic may be reversed (e.g., an association between leverage and incidence of default due to financial distress as opposed to insolvency, which all else equal implies higher recoveries). In the context of creditors foreclosing upon the firm, an optimal boundary may be elevated for more leveraged firms, resulting in mitigated recovery risk (Carey and Gordy [2007]). Tobin’s Q exhibits economic significance of about the same order as the leverage ratio, having a partial effect of 0.073. The intuition here for a positive relationship with LGD is that investors in these far less than efficient markets are grossly overvaluing these firms prior to default, and in spite of whatever mechanism gives rise to such speculative froth (e.g., informational asymmetries), this is reversed at post default as recovery uncertainty is reduced. The intangibles ratio achieves economic significance at a partial effect of 0.098, implying that a doubling of this ratio

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respectively. This is a little disappointing, as we would expect to see improvement for instrument-level predictive accuracy on at least an in-sample basis. However, there is evidence of more accurate prediction of instrument LGD in looking at the Hoshmer–Lemeshow (HL) statistics. While for obligor LGD the p-value in-sample is 0.55, out-of-sample it is 0.43. However, in the discriminatory accuracy measures, in both equations we see robust magnitudes of areas under ROC curves: 0.8920 in-sample versus 0.8876 out-of-sample in the obligor equation; and 0.9010 versus 0.8292, in and out of sample, respectively, in the instrument equation. However, the Kolmogorov–Smirnov p-values show good separation, but we note that they are about one-tenth of the values in the obligor as compared to the instrument equation in-sample.

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Discussion and Conclusions

In this study we empirically investigate ultimate loss given default by studying its determinants. In the process, we build a predictive econometric model and evaluate the rank ordering and predictive accuracy properties of this model. We use a sample of 871 large corporate bankruptcies and out-of-court settlements on firms rated by Moody’s in the 1985–2008 period for which the complete capital structures are available. We contribute to the literature on LGD along several dimensions: understanding it at different levels (obligor versus instrument), finding a comprehensive set of determinants, and evaluating our econometric models rigorously according to well-accepted measures of model performance on out-of-sample basis. Furthermore, we have tried to propose a framework that would prove useful to traders of distressed debt, risk managers, and supervisors. Our main contribution to the literature is along two broad dimensions. First, we construct a robust econometric model that can coherently model the theoretically motivated interplay between LGD at the obligor and instruments levels. Second, we conduct an empirical quest for a set of determinants of ultimate LGD, motivated by both corporate finance theories and risk management practices. The contribution along the dimension of model development is manifest in several stages. First, we implement an improved econometric methodology by analyzing the ultimate LGD through estimating a model in the BLGLM class, which has some desirable ­properties

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debt above and below in the capital structure are in line with expectations and precisely measured, with respective partial effects of 0.12 and -0.29. The strength of the debt cushion measures is consistent with theoretical predictions (Carey and Gordy [2007]) and empirical findings (Keisman and van de Castle [2000]). Addressing the firm capital structure variables appearing only in the obligor equation, note that results are in line with previous results and robust in economic and statistical significance. The number of creditor classes is significantly and inversely associated with the ultimate LGD, with a partial effect of -0.08. This is intuitive if the number of instruments is viewed as a proxy for the capital structure complexity of a firm, which we would expect to be associated with a more difficult or drawn-out resolution process, and consequently a higher economic LGD. Similarly, the proportion of secured debt is economically and statistically significant, having a partial effect of -0.13. Lastly for this group, the proportion of bank debt in the capital structure is also economically and statistically significant, with a partial effect of -0.23, also consistent with intuition regarding the power of the firm’s secured or senior creditors. The final set of variables that we discuss measures time periods of relevance, the (maximum) time between instrument defaults appearing in the obligor equation, as well as the time to maturity at the time of default appearing in only the instrument equation. The time between defaults is notably weaker in economic significance, as suggested by the univariate analysis, but precisely estimated, having a partial effect of -0.16. However, time to maturity at default is of nearly the same economic significance as suggested in exploratory analysis, with a partial effect of -0.013. We interpret this as in line with various well-known seasoning effects in the default prediction literature, where earlier default may be indicative of a weaker credit risk profile, which in turn can imply higher loss severity. We conclude this section by a discussion of the model diagnostics for the FIML simultaneous equation estimation (Exhibit 3). The broad fit to the data of this model as measured by the likelihood ratio is robust at conventional significance levels. The in-sample R-squared is lower in the instrument equation but almost the same in the obligor equation, 0.66 versus 0.70, respectively. However, out-of-sample this is reversed, with the improvement in the obligor equation but negligible difference in the instrument equation, 0.51 versus 0.45, Summer 2011

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episodes significantly inf luence LGD at the obligor level, consistent with evidence presented by Carey and Gordy [2007]. Considering industry-specific factors, we find industry profit margin and dummy variables for the technology or utility industries to be significant, consistent with Acharya et al. [2007] and evidence of the independent importance of a separate systematic factor governing LGD apart from that driving default (Frye [2000a, 2000b, 2000c]). These findings contribute to our understanding of the degree of systematic risk present in this asset class of defaulted fixed income instruments; there are also implications for the Basel II regulatory capital regulations, in which financial institutions must assess the degree to which LGD on their portfolios may be elevated in periods of economic downturn. We also demonstrate the economic and statistical significance of firm-specific effects, as measured by financial variables in the obligor equation. In particular, measures of firm size, leverage, tangibility, market valuation, cash f low, and liquidity are all found to significantly and inversely inf luence the ultimate LGD. Furthermore, we document a new finding: Larger firms have significantly lower LGDs and larger loans significantly higher LGDs. The economic import of this lies in the quantification of idiosyncratic risk associated with this asset class and the utility of such factors in helping market participants better inform their expectations. We further find that contractual features are economically and statistically significant determinants of facility LGD: a better ranking of collateral, less debt above/more debt below, and relative seniority of creditor class are all associated with lower LGD. This confirms findings of Keisman and van de Castle [2000] with regard to the importance of loan structure in determining recoveries, which again speaks to an augmented understanding of the idiosyncratic components of recoveries. Finally, we also find that capital structure variables exert particular inf luences on LGD: The number of creditor classes and proportions of secured and bank debt are all significantly and inversely related to the ultimate LGD. The latter finding is consistent with the finding by Carey and Gordy [2007], while the first two are new to the literature, and the first result is the opposite of the finding in Acharya et al. [2007]. The result on debt composition is important from the finance perspective of better understanding the role of financial institutions in contributing to the efficiency of markets through

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relative to alternative approaches (e.g., approximate linear regression model of a normal transformed LGD), including better overall model performance and quality of coefficient estimates. We focus on the obligor-level LGD, similarly to Carey and Gordy [2007], building upon their intuition that facility level recoveries can be likened to collar options on the estate level recovery. This involves extending prior work by modeling the ultimate loss given default jointly at the firm and instrument levels. To implement this econometrically, we build a simultaneous equation (full information, maximum likelihood—FIML) version of BLGLM. Finally, the model is validated rigorously on an out-of-time and out-ofsample framework. The next contribution is analysis of new as well as previously considered explanatory variables in a unified framework. We confirm many of the stylized facts and findings of the literature in regard to the determinants of the ultimate LGD and find, in addition, the independent significance of macroeconomic factors, industry conditions, equity returns, and the price of traded debt at default. We demonstrate the statistical and economic significance of debt and equity market determinants of LGD: price of instrument debt at default in the instrument LGD equation, the principal weighted obligor LGD at default, and cumulative abnormal returns on equity prior to default, the latter two in the obligor LGD equation. The economic implication is that there may be information embedded in the market beyond that distilled from the traditional style of credit analysis that workout specialists or vulture investors may undertake. That is, for defaulted bonds and loans of companies that have either traded debt or equity, incorporation of market signals may improve forecasts of expected recoveries. We also find that firms having been investment grade at origination have significantly lower ultimate LGDs, consistent with recent research (Cantor et al. [2007]). We interpret this as evidence that ratings assessments may contain information on not only default likelihood, but more broadly some notion of expected credit loss, which embeds losses in the event of default. Regarding macroeconomic and industry-wide effects, we find both the aggregate default rate (Moody’s trailing 12-month speculative) and a measure of the economic growth (S&P 500 returns) to significantly inf luence the ultimate LGD through the impact on the obligor equation. Over and above this, we find that dummy variables for the 2000–2002 and the 1991–1992 recessionary

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their role in optimally monitoring lenders in the face of potential informational imbalances.

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We would like to thank participants of the 2007 FMA Annual Meeting and the Comptroller of the Currency/Risk Analysis Division seminar as well as Jon Frye, Kick Kiefer, and Min Qi. The views expressed herein are those of the authors and do not necessarily represent a position taken by the Office of the Comptroller of the Currency or the U.S. Department of the Treasury. 1 LGD is equivalent to 1 minus the recovery rate, dollar recovery as a proportion of par, or exposure at default assuming all debt becomes due at default. We focus on LGD as opposed to recoveries with a view toward credit risk management applications. 2 Acharya, Bharath, and Srinivasan [2007]; Altman, Resti, and Sironi [2001, 2003]; Altman and Fanjul [2004]; Altman and Ramayanam [2006]; Araten, Jacobs, and Varshney [2004]; Carey and Gordy [2007]; Frye [2000a, 2000b, 2000c]; and Jarrow [2001]. 3 Median LGDs of 49.5% and 66.5% for defaulted issuers originally investment and speculative grades, respectively. 4 Altman [2006] reported that his model overpredicts LGD in recent years, which he speculated may be due to bubble conditions in the high-yield market. 5 Also see Ohlson [1980]. 6 In this application, a mixture of two beta distributions is found to be sufficient to model LGD, as results for a mixture of three or four were not materially different while involving an order of magnitude greater computational overhead; beyond four, estimates were unstable (results available upon request.) 7 Results obtained from either OLS or Tobit regressions are qualitatively similar and are available upon request. 8 A statistical analysis, available upon request, shows that the final datasets used in the regression analyses are demographically similar to the broader MURD database. 9 In the case of debt, we take the average price from the 15th to the 45th day after default from the Moody’s Default Risk Service (DRS™) database. For financials and equity prices, we look to Compustat or CRSP in either the nearest quarterly filing date or month prior to default, respectively. 10 We also replicate results with a risk-free term structure, as in Carey and Gordy [2007], as well as using a highyield index, as in Acharya et al. [2007], and the results are not materially different. 11 Previous research found that while market implied LGD has predictive power for ultimate LGD, it is an upwardly biased estimator, which has been ascribed to either the illi-

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Endnotes

quidity of defaulted debt markets, investors’ extreme risk aversion, or even an over-shooting effect. 12 This observation is consistent with the predictions of several theoretical models of the resolution of default (e.g., Parnes [2009]). 13 We calculate 12-month CAR at each date in the 90 days prior to default using the CRSP NYSE/AMEX/NASDAQ equally weighted market index as the benchmark. 14 An alternative explanation involves the empirical asset pricing results of Vassalou and Xing [2004], who found that the Fama and French [1992] size and value premia were concentrated among the companies having the highest default risk. If we assume a negative relationship between recovery risk and default risk (as in standard versions of the Merton [1974] structural model of credit risk), then it may be that larger and more highly valued companies nearing default would have lower premia and higher prices leading up to default, as well as higher than average ultimate recoveries. This is because our CARs are measured prior to default, whereas the excess returns of Vassalou and Xing measured this ex ante according to the default risk indicator (DIA) that they developed.

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Altman, E.I. “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy.” Journal of Finance, 23 (1968), pp. 589-609. ——. “Default Recovery Rates and LGD in Credit Risk Modeling and Practice: An Updated Review of the Literature and Empirical Evidence.” Working paper, NYU Salomon Center, 2006. Altman, E.I., and A. Eberhart. “Do Seniority Provisions Protect Bondholders’ Investments?” The Journal of Portfolio Management, Summer 1994, pp. 67-75. Altman, E.I., and G. Fanjul. “Defaults and Returns in the High Yield Bond Market: Analysis through 2003.” Working paper #S-0304, New York University Salomon Center, 2004. Altman, E.I., and V.M. Kishore. “Almost Everything You Wanted to Know about Recoveries on Defaulted Bonds.” Financial Analysts Journal, Nov/Dec. 1996, pp. 57-64.

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